Microwave Surface Impedance Research Articles

Power-dependent impedance of high temperature superconductor thin films: Relation to harmonic generation

We present measurements of the power-dependent microwave surface impedance of YBa2Cu3O7−δ thin films, performed using patterned coplanar waveguide (CPW) resonators at 5.87 GHz and 76 K. We compare these resonator measurements with third-harmonic generation measurements performed on CPW transmission lines of the same geometry patterned onto the same thin-film sample at the same frequency and temperature. We find that the power-dependent surface reactance Xs(Prf) is directly related to the magnitude of the generated third-harmonic signal, indicating a common origin for both of these manifestations of nonlinearity in high temperature superconductor (HTS) devices. These results are consistent with the nonlinear response generated by a current-dependent penetration depth λ(J), which provides a material limitation on the linearity that can be achieved in any practical HTS microwave device.

An anomalous weak link model for microwave surface impedance ofYBa2Cu3O7-δ films in a weak dc magnetic field

By incorporating an anomalous weak link (AWL), the coupled-grainmodel is modified to describe the anomalous decrease of microwave surfaceimpedance (Zs) of YBa2Cu3O7-δ thin films in aweak dc magnetic field (Bdc). The critical current density of the AWL hasa minimum at zero Bdc, a linear dependence on Bdc for low Bdcand a saturation at high Bdc, unlike a conventional weak link. Using thismodel, the field dependences of surface resistance are calculated at differentrf input powers and resonant modes. The dimensionless parameters rH,defined as the ratio of the change of surface resistance and reactance, arealso computed. The simulation results agree with the measurementqualitatively. We believe that the anomalous Zs behaviour may originatefrom the AWL.

Microwave response of high-T c superconducting crystals: Results, problems, and prospects

The results of studying temperature behavior of the microwave surface impedance Z s (T) and conductivity tensor $$\hat \sigma (T)$$ (T) of high-T c superconducting (HTSC) single crystals are analyzed. The emphasis is on the experimental facts that are inconsistent with the known electrodynamic concepts of conductivity mechanisms in these materials. Possible reasons for the inconsistency are discussed in the context of structural features of the HTSC crystals, and the outlook for future investigations is outlined.

Microwave electrodynamics of the antiferromagnetic superconductor GdBa 2Cu 3O 7−δ

The temperature dependence of the microwave surface impedance and conductivity are used to study the pairing symmetry and properties of cuprate superconductors. However, the superconducting properties can be hidden by the effects of paramagnetism and antiferromagnetic long-range order in the cuprates. To address this issue we have investigated the microwave electrodynamics of GdBa 2Cu 3O 7−δ, a rare-earth cuprate superconductor which shows long-range ordered antiferromagnetism below T N = 2.2K, the Neel temperature of the Gd ion subsystem. We measured the temperature dependence of the surface resistance and surface reactance of c-axis oriented epitaxial thin films at 10.4, 14.7 and 17.9 GHz with the parallel plate resonator technique down to 1.4 K. Both the resistance and the reactance data show an unusual upturn at low temperature and the resistance presents a strong peak around T N mainly due to change in magnetic permeability.

Non-quasiparticle microwave absorption in Bi2Sr2CaCu2O8+δ

We show that a non-quasiparticle charge collective mode, in parallel and coincident with the d-wave pair conductivity, leads to a quantitative understanding of microwave surface impedance measurements on superconducting Br 2 Sr 2 CaCu 2 O 8+δ. The analysis suggests an inhomogeneous chrge ground state in Bi 2 Sr 2 CaCu 2 O 8+δ and other HTS.

Microwave excitation of Josephson plasma mode and Swihart waves in vortex state of YBa 2Cu 3O 6.9 ceramics

The narrow peak of microwave absorption and a jump of reactive component of surface impedance were observed in YBa 2 Cu 3 O 6.9 ceramics near critical temperature T KT =88–89 K in zero magnetic field and were interpreted as the Kosterlitz-Thouless phase transition. In higher fields a wide step of the strong absorption is formed, which is transformed with increasing H into the wide absorption peak near 85 K at the resonance field H o=3,5 kOe . The temperature oscillations of Z(T) below T c were observed. It is supposed that these peculiarities of microwave surface impedance are connected with resonance excitation of the Josephson plasma mode and Swihart waves.

Magnetic-field-induced anomalous microwave response in superconducting YBa2Cu3O7−δ thin films

The magnetic-field-induced decrease of microwave surface impedance, Zs=Rs+jXs, of superconducting YBa2Cu3O7−δ thin films is investigated using a microstrip resonator technique. Through measuring Zs as the direct current (dc) magnetic field is increased from zero to a certain value Hmax and subsequently decreased back to zero, it is found that Zs(Hdc) is totally reversible if Hmax does not exceed the threshold field H*, at which Rs shows a minimum, while it is irreversible if Hmax is larger than H*. It is confirmed that the anomalous effect happens in a vortex-free state. The threshold field H* is identified with the lower critical field for the vortices penetrating into the superconducting thin films. The anomalous effect is believed to be mainly contributed by the imperfect microstructure of the superconducting thin films.

Microwave Electrodynamics of low TC and high TC Systems with Coexisting Superconductivity and Magnetism

We investigate the microwave electrodynamics of both artificial low T C superconducting/magnetic (S/M) layered structures and high T C cuprates. In particular we focus on Nb/CuMn (superconducting/spin-glass) bilayers, and on GbBa 2 Cu 3 O 7-δ (GBCO) thin films, which show coexistence of superconductivity and long range ordered antiferromagnetism below T N = 2.2 K . In both cases we are interested in the influence of magnetism on superconducivity. Moreover, in the GBCO case, we want to shed light on the problem of the determination of the pairing symmetry in the cuprates. First we show surface impedance data at 10 GHz on Nb/CuMn bilayers. We extract information about the induced order parameter in the magnetic layer and we compare it with the exotic behavior predicted for S/M proximity systems. Then we present microwave surface impedance data at three different frequencies on GBCO c-axis oriented epitaxial thin films. Both the resistance and the reactance data on GBCO show an unusual low temperature behavior, mainly due to change in magnetic permeability. This result indicates that the paramagnetism of the rare-earth ions has to be taken into account when extracting the superconducting penetration depth as a function of temperature, and thus determining the pairing state symmetry of the cuprates.

Phenomenological description of the microwave surface impedance and complex conductivity of high-T c single crystals

Measurements of the microwave surface impedance Z s (T) = R s (T) + iX s (T) and the complex conductivity σs(T) in the ab-plane of high-quality high-T c YBCO, BSCCO, TBCCO, and TBCO single crystals are analyzed. Experimental data of Z s (T) and σs(T) are compared with calculations based on a modified two-fluid model that includes a temperature-dependent quasiparticle scattering and a unique temperature variation of the density of superconducting carriers. We describe the agreement and disagreement of our analysis with the salient features of the experimental data. We review the existing microscopic models based on unconventional symmetry types of the order parameter and on novel quasiparticle relaxation mechanisms.

Anisotropic microwave resistance ofYBa2Cu3O6.95and the modified two-fluid model

The modified two-fluid model of the microwave surface impedance Zs5Rs1iXs of cuprates is discussed in Refs. 1‐6 with regard to the temperature dependence of Zs(T )i n the ab plane for different optimally doped high-Tc single crystals. Here, we apply our model to the anisotropic microwave properties of high-quality single crystals of YBa2Cu3O6.95 ~YBCO!. The real part of the surface impedance Re@Zs#5Rs is a measure of the microwave power absorbed. With the definition s5(s8/s9) 2 , where s8 and s9 are the real and imaginary parts of the conductivity, the real part of Zs is

Microwave surface impedance in overdoped Tl 2Ba 2CuO 6+ δ

The microwave surface impedance Z s= R s+i X s and transmittivity T H ′ of overdoped Tl 2Ba 2CuO 6+ δ have been measured in a magnetic field up to 7 T in order to clarify the unusual temperature dependence of the DC resistive-transition field H ∗ . From the result of T H ′, columnar defects enhance H ∗ , indicating that H ∗ is the melting point of vortices instead of the mean field H c2. The field dependence of R s is found to be unusual as compared with that expected from the result of the DC resistivity.

Microwave surface impedance of high- Tc single crystals

Results of recent investigations are analyzed pertaining to the real and imaginary parts of the surface impedance Z s= R s+i X s of high-quality, high- T c single crystals of YBa 2 Cu 3 O 6.95, Ba 0.6 K 0.4 BiO 3, Tl 2 Ba 2 CaCu 2 O 8−δ, Tl 2 Ba 2 CuO 6+δ , and Bi 2Sr 2CaCu 2O 8. Characteristic features of the temperature dependence of the surface impedance are pointed out. Published models are mentioned which investigate the typical features of these materials.

Single-feed superconducting circularly polarized microstrip arrayantenna for direct-to-home receiving system

Single-feed circularly polarized microstrip patch and patcharray antennas for `direct-to-home' receiving system at around12 GHz are studied by theoretical analysis and experiments. A full-wavemicrowave circuit simulator (Em), based on the method of moments andcapable of handling the microwave surface impedance, has been used in thetheoretical analysis of the antennas. Antennas have been fabricated fromboth normal conductor (gold) and YBa2Cu3O7-x(YBCO) superconductor for comparison. Measured results on resonantfrequency (fr), return loss, gain, bandwidth, and axial ratioare presented. The antennas are found to show a very low axial ratio and amoderate bandwidth. In the comparison of gain, the superconducting antennasshowed a remarkable improvement over their gold counterparts. The receivingpower of a four-element array fabricated from a single-side YBCO thin filmon (100) MgO single crystal substrate is found to be 1.8 dB higher thanthat of a gold array with identical configuration and both measured at 77 K.

Phenomenological model of the microwave surface impedance ofhigh-Tc superconducting films

A modified phenomenological model of the microwave surface impedanceis proposed. The model is based on the experimental data of measurements ofthe microwave characteristics of high-temperature superconducting (HTS) films.Numerous experimental results are analysed. The model description of the HTSsingle crystals and the HTS epitaxial films are compared. It is shown thatthese two objects are of different physical nature and should be described bydifferent models. The phenomenological model of the HTS film surface impedancebased on the modified two-fluid model takes into account specific features ofthe HTS films. The model of the real and imaginary parts of the surfaceimpedance uses the model parameter γ, which is responsible for thesuperconducting and normal charge carrier density. This parameter is used fora description of the temperature dependence of the London penetration depthλL(T) including λL(0). The relaxation time model also usesthe γ parameter in combination with the residual resistance parameterα. One can conclude that the parameter γ is the maincharacteristic of the model and can be considered as a figure of merit of theHTS film microwave properties.

Laterally resolved microwave surface-resistance measurement of high-T/sub c/ superconductor samples by cavity substitution technique

Microwave surface impedance measurement of a high-temperature superconductor (HTS) is a sensitive probe to test its quality, particularly if a microwave device is to be fabricated. Most microwave characterization employs resonance techniques in which the components of the surface impedance are extracted from the measured Q value and the shift in the resonance frequency. In this paper, we present a modification of the widely used complete end-plate substitution technique to measure the surface resistance of samples having dimensions smaller than the dimension of the end plate at 20 GHz, as well as to facilitate the laterally resolved surface resistance measurement of large-area HTS samples. From the knowledge of the electromagnetic-field configuration in a TE/sub 011/-mode cylindrical cavity, the loss contribution from the HTS sample is analyzed theoretically and measured experimentally in the temperature range of 20-100 K. The design of the cavity is discussed to optimize the sensitivity of the measurement by the placement of the sample and to maximize the difference in the measured Q value.

Precise measurement of the microwave surface impedance of a YBa2Cu3O7−δ film on copper substrate

In measurement of the microwave surface resistance, Rs(T), of a high-Tc film with a host-cavity method, in which the cavity material is usually copper, the systematic error in Rs at low temperature can be significantly reduced through calibration with the data obtained by a niobium host cavity. Using a cavity excited in the TE011 mode at 13.6 GHz, the procedure is illustrated for a c-axis oriented YBa2Cu3O7−δ film fabricated on 36 mm diameter copper disk with yttria-stabilized-zirconia and chromium buffer layers. The temperature dependence in Rs(T) was consistent with that of the penetration depth; both quantities behavior could be fit well by a modified two-fluid model, in which the fraction of the pairing normal carriers obeyed (T/Tc)2 rather than (T/Tc)4 with some 20% of the charge carriers remaining normal.

Coherence effects in conventional layered superconductors

We present and apply a theory for the coherence effects in spatially inhomogeneous layered superconductors. The theory is based upon a comparison of de Gennes's self-consistent equation for the pair potential to that of alternative proximity-effect models, from which the generalized, space-dependent BCS probability amplitudes u's and v's are obtained. Recent microwave surface impedance data of Pambianchi et al. on Nb/Cu bilayers are successfully reproduced.

Microwave surface impedance ofYBa2Cu3O6.99: Comparison of theory and experiment

Surface resistance experiments by the Vancouver group on very high quality single crystals of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.99}$ are compared with a model proposed by Trunin et al. and the author. The resistance measurements are from $1.14$ to $75.3$ GHz, and good numerical agreement is found over that frequency interval for all temperatures. From these measurements the real part of the microwave conductivity ${\ensuremath{\sigma}}^{\ensuremath{'}}(T)$ was extracted, and from it a Drude-like conductivity spectrum was obtained below $25$ K, all in agreement with the model. From the conductivity spectrum the scattering rate of the thermally excited quasiparticles was found to increase with temperature $(T),$ in agreement with a Gr\"uneisen T dependent intrinsic resistivity at low temperatures.

Determination of the magnetization scaling exponent for single-crystalLa0.8Sr0.2MnO3by broadband microwave surface impedance measurements

Employing a broadband microwave reflection configuration, we have measured the complex surface impedance, $Z_S(\omega,T)$, of single crystal La$_{0.8}$Sr$_{0.2}$MnO$_3$, as a function of frequency (0.045-45 GHz) and temperature (250-325 K). Through the dependence of the microwave surface impedance on the magnetic permeability, $\hat\mu(\omega,T)$, we have studied the local magnetic behavior of this material, and have extracted the spontaneous magnetization, $M_0(T)$, in {\em zero applied field}. The broadband nature of these measurements and the fact that no external field is applied to the material provide a unique opportunity to analyze the critical behavior of the spontaneous magnetization at temperatures very close to the ferromagnetic phase transition. We find a Curie temperature $T_C=305.5\pm 0.5$ K and scaling exponent $\beta=0.45\pm 0.05$, in agreement with the prediction of mean-field theory. We also discuss other recent determinations of the magnetization critical exponent in this and similar materials and show why our results are more definitive.

The nonlinear surface impedance of YBa2Cu3O7−δ thin films in zero and large applied fields

We present coplanar resonator measurements of the nonlinear microwave surface impedance of laser ablated and electron-beam coevaporated YBa2Cu3O7−δ thin films at 8 GHz in zero and applied magnetic fields, including the effects of irradiation with heavy ions. Correlations between the changes in surface resistance and reactance as a function of microwave current suggest that there are different contributions to the nonlinear behavior at low and high microwave currents in both zero and applied fields. In zero field, we suggest that microwave-induced flux lines are responsible for the observed nonlinear behavior, resulting in thermal runaway at large, sample dependent, microwave currents. The observed nonlinearity completely masks any possible contribution from the intrinsic pair breaking expected for a d-wave superconductor. In a magnetic field at relatively low currents, the nonlinearity can be described by the nonlinear dynamics of flux lines pinned by defects with a continuous range of pinning strengths. At higher currents, microwave field nucleation of flux lines is again considered important. On irradiation with 3.6 MeV/nucleon Xe-129 ions, the microwave losses and nonlinearity are significantly decreased in both zero and applied fields, which could have important implications for microwave device applications.